RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-12-09_03:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.79 22.7479 0.842362 2 to 25 15.81 18.8118 0.660559 3 to 26 15.91 28.4392 0.959940 4 to 27 15.90 20.0975 0.730730 5 to 28 15.73 20.7243 0.761136 6 to 29 15.83 14.7297 0.385056 7 to 30 15.60 23.5632 0.868203 8 to 31 15.62 19.4644 0.697464 9 to 32 15.53 20.0979 0.730748 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.016620 Tough bday spacings test for dh-ranFile-2016-12-09_03:31: 4096 birthdays, year=2^32 days Table of Expected vs. Observed counts: Duplicates 0 1 2 3 4 5 6 7 8 9 >=10 Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1 Observed 6 32 84 87 109 83 44 28 17 4 6 (O-E)^2/E 1.1 0.6 1.6 1.2 1.3 0.3 1.3 0.1 0.3 1.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 9.647, p= 0.528 RESULTS OF GCD FOR dh-ranFile-2016-12-09_03:31 Euclid's algorithm: p-value, steps to gcd: 0.276020 p-value, dist. of gcd's: 0.261186 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-12-09_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.071 0.140 0.409 0.283 0.962 0.639 0.615 0.834 Bits 8 to 15---> 0.216 0.941 0.675 0.027 0.135 0.980 0.109 0.865 Bits 16 to 23---> 0.729 0.492 0.052 0.209 0.932 0.419 0.658 0.226 Bits 24 to 31---> 0.286 0.775 0.925 0.926 0.550 0.521 0.050 0.215 KS test for the above 32 p values: 0.340 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-12-09_03:31, p-values for 5 runs: 0.3318, 0.2777, 0.3440, 0.5057, 0.1307 Rank test for binary matrices (31x31) for dh-ranFile-2016-12-09_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 204 211.4 0.260 0.260 r= 29 5119 5134.0 0.044 0.304 r= 30 23212 23103.0 0.514 0.818 r= 31 11465 11551.5 0.648 1.466 chi-square = 1.466 with df = 3; p-value = 0.310 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-12-09_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 200 211.4 0.617 0.617 r= 30 5111 5134.0 0.103 0.720 r= 31 23075 23103.0 0.034 0.754 r= 32 11614 11551.5 0.338 1.092 chi-square = 1.092 with df = 3; p-value = 0.221 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-12-09_03:31 b-rank test for bits 1 to 8, p=0.93715 b-rank test for bits 2 to 9, p=0.56730 b-rank test for bits 3 to 10, p=0.12656 b-rank test for bits 4 to 11, p=0.65651 b-rank test for bits 5 to 12, p=0.22041 b-rank test for bits 6 to 13, p=0.92992 b-rank test for bits 7 to 14, p=0.61732 b-rank test for bits 8 to 15, p=0.10799 b-rank test for bits 9 to 16, p=0.41047 b-rank test for bits 10 to 17, p=0.57739 b-rank test for bits 11 to 18, p=0.18737 b-rank test for bits 12 to 19, p=0.74286 b-rank test for bits 13 to 20, p=0.64638 b-rank test for bits 14 to 21, p=0.80744 b-rank test for bits 15 to 22, p=0.48002 b-rank test for bits 16 to 23, p=0.12059 b-rank test for bits 17 to 24, p=0.57383 b-rank test for bits 18 to 25, p=0.85916 b-rank test for bits 19 to 26, p=0.99804 b-rank test for bits 20 to 27, p=0.75607 b-rank test for bits 21 to 28, p=0.25122 b-rank test for bits 22 to 29, p=0.79863 b-rank test for bits 23 to 30, p=0.73040 b-rank test for bits 24 to 31, p=0.04508 b-rank test for bits 25 to 32, p=0.79836 TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices The above should be 25 uniform [0,1] random variables: The KS test for those 25 supposed UNI's yields p = 0.449938 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-12-09_03:31 (20 bits/word, 2097152 words 20 bitstreams. No. missing words should average 141909.33 with sigma=428.00.) ---------------------------------------------------------------- BITSTREAM test results. Bitstream No. missing words z-score p-value 1 141701 -0.49 0.313217 2 141721 -0.44 0.329960 3 142068 0.37 0.644579 4 141786 -0.29 0.386614 5 141107 -1.87 0.030424 6 141953 0.10 0.540635 7 141881 -0.07 0.473613 8 142483 1.34 0.909934 9 141644 -0.62 0.267652 10 142180 0.63 0.736439 11 142097 0.44 0.669481 12 141682 -0.53 0.297659 13 141432 -1.12 0.132370 14 142020 0.26 0.602018 15 142018 0.25 0.600214 16 141948 0.09 0.535996 17 141667 -0.57 0.285632 18 142278 0.86 0.805485 19 142285 0.88 0.809956 20 142058 0.35 0.635840 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-12-09_03:31 Bits used No. missing words z-score p-value 23 to 32 141376 -1.8391 0.032953 22 to 31 141767 -0.4908 0.311786 21 to 30 141596 -1.0804 0.139971 20 to 29 141798 -0.3839 0.350528 19 to 28 141704 -0.7080 0.239462 18 to 27 142210 1.0368 0.850084 17 to 26 142051 0.4885 0.687408 16 to 25 142264 1.2230 0.889335 15 to 24 141978 0.2368 0.593591 14 to 23 141886 -0.0804 0.467940 13 to 22 141660 -0.8598 0.194961 12 to 21 141835 -0.2563 0.398856 11 to 20 141810 -0.3425 0.365981 10 to 19 142083 0.5989 0.725368 9 to 18 142131 0.7644 0.777679 8 to 17 141776 -0.4598 0.322845 7 to 16 141731 -0.6149 0.269300 6 to 15 142342 1.4920 0.932146 5 to 14 142047 0.4747 0.682508 4 to 13 141921 0.0402 0.516050 3 to 12 142100 0.6575 0.744565 2 to 11 142221 1.0747 0.858751 1 to 10 141748 -0.5563 0.288999 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-12-09_03:31 Bits used No. missing words z-score p-value 28 to 32 141499 -1.3909 0.082120 27 to 31 141576 -1.1299 0.129252 26 to 30 141789 -0.4079 0.341674 25 to 29 142283 1.2667 0.897365 24 to 28 141476 -1.4689 0.070928 23 to 27 141146 -2.5876 0.004833 22 to 26 141602 -1.0418 0.148753 21 to 25 141522 -1.3130 0.094594 20 to 24 142153 0.8260 0.795598 19 to 23 141657 -0.8554 0.196177 18 to 22 141924 0.0497 0.519831 17 to 21 141601 -1.0452 0.147968 16 to 20 141961 0.1752 0.569520 15 to 19 141788 -0.4113 0.340431 14 to 18 141660 -0.8452 0.199003 13 to 17 141923 0.0463 0.518480 12 to 16 142022 0.3819 0.648744 11 to 15 142183 0.9277 0.823217 10 to 14 142187 0.9413 0.826713 9 to 13 142371 1.5650 0.941207 8 to 12 142307 1.3480 0.911176 7 to 11 142447 1.8226 0.965819 6 to 10 141904 -0.0181 0.492792 5 to 9 141787 -0.4147 0.339189 4 to 8 142314 1.3718 0.914931 3 to 7 141674 -0.7977 0.212514 2 to 6 141812 -0.3299 0.370726 1 to 5 142231 1.0904 0.862233 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-12-09_03:31 Bits used No. missing words z-score p-value 31 to 32 141690 -0.6470 0.258819 30 to 31 141884 -0.0747 0.470219 29 to 30 141793 -0.3432 0.365740 28 to 29 141560 -1.0305 0.151394 27 to 28 141535 -1.1042 0.134749 26 to 27 141968 0.1731 0.568701 25 to 26 141828 -0.2399 0.405199 24 to 25 141869 -0.1190 0.452651 23 to 24 141888 -0.0629 0.474915 22 to 23 141774 -0.3992 0.344872 21 to 22 142043 0.3943 0.653323 20 to 21 142561 1.9223 0.972718 19 to 20 141413 -1.4641 0.071583 18 to 19 141648 -0.7709 0.220388 17 to 18 142130 0.6509 0.742459 16 to 17 141914 0.0138 0.505496 15 to 16 141748 -0.4759 0.317073 14 to 15 141987 0.2291 0.590610 13 to 14 141762 -0.4346 0.331926 12 to 13 141508 -1.1839 0.118233 11 to 12 142337 1.2616 0.896447 10 to 11 142277 1.0846 0.860944 9 to 10 142256 1.0226 0.846758 8 to 9 141852 -0.1691 0.432853 7 to 8 141968 0.1731 0.568701 6 to 7 142361 1.3324 0.908629 5 to 6 142433 1.5447 0.938797 4 to 5 141811 -0.2901 0.385886 3 to 4 141515 -1.1632 0.122371 2 to 3 141474 -1.2842 0.099543 1 to 2 141927 0.0521 0.520785 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-12-09_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2498.00 -0.028 0.488706 Test results for specific bytes for dh-ranFile-2016-12-09_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2564.29 0.909 0.818388 2 to 9 2528.72 0.406 0.657705 3 to 10 2466.89 -0.468 0.319787 4 to 11 2422.49 -1.096 0.136509 5 to 12 2701.90 2.855 0.997850 6 to 13 2567.42 0.953 0.829826 7 to 14 2421.63 -1.108 0.133875 8 to 15 2537.26 0.527 0.700859 9 to 16 2510.73 0.152 0.560320 10 to 17 2506.34 0.090 0.535719 11 to 18 2447.38 -0.744 0.228398 12 to 19 2501.22 0.017 0.506910 13 to 20 2525.62 0.362 0.641470 14 to 21 2467.78 -0.456 0.324326 15 to 22 2422.78 -1.092 0.137410 16 to 23 2491.92 -0.114 0.454525 17 to 24 2492.45 -0.107 0.457483 18 to 25 2493.41 -0.093 0.462854 19 to 26 2557.81 0.818 0.793189 20 to 27 2486.66 -0.189 0.425193 21 to 28 2547.21 0.668 0.747799 22 to 29 2547.19 0.667 0.747749 23 to 30 2542.48 0.601 0.726009 24 to 31 2461.40 -0.546 0.292564 25 to 32 2561.01 0.863 0.805887 CDPARK for dh-ranFile-2016-12-09_03:31: result of 10 tests (Of 12000 tries, the average no. of successes should be 3523.0 with sigma=21.9) No. succeses z-score p-value 3491 -1.4612 0.071982 3568 2.0548 0.980051 3513 -0.4566 0.323972 3553 1.3699 0.914635 3525 0.0913 0.536383 3501 -1.0046 0.157553 3493 -1.3699 0.085365 3540 0.7763 0.781201 3525 0.0913 0.536383 3562 1.7808 0.962529 Square side=100, avg. no. parked=3527.10 sample std.=26.61 p-value of the KSTEST for those 10 p-values: 0.490996 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-12-09_03:31 0.8403,0.7422,0.5305,0.3292,0.9647,0.9895,0.9206,0.8695,0.1469,0.8068, The KS test for those 10 p-values: 0.019108 The 3DSPHERES test for dh-ranFile-2016-12-09_03:31 sample no r^3 equiv. uni. 1 2.779 0.088486 2 79.748 0.929930 3 37.305 0.711624 4 12.357 0.337599 5 5.723 0.173668 6 63.026 0.877648 7 91.867 0.953216 8 6.145 0.185225 9 21.515 0.511863 10 14.290 0.378949 11 4.396 0.136290 12 25.420 0.571448 13 39.409 0.731161 14 14.931 0.392065 15 28.480 0.613002 16 9.840 0.279632 17 1.161 0.037964 18 11.347 0.314928 19 26.872 0.591698 20 2.791 0.088841 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.738473 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-12-09_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 1.8 0.8 0.8 0.0 -0.6 0.1 -0.3 0.1 -0.3 -0.7 0.3 -0.3 -0.4 0.7 0.3 0.7 -0.4 -0.4 -1.0 -0.1 -0.3 -0.6 0.5 -0.1 1.0 1.1 -0.1 1.2 1.2 1.0 -1.1 0.3 -1.3 2.3 -2.1 0.5 0.2 -1.6 1.5 1.6 1.0 -1.1 Chi-square with 42 degrees of freedom:37.887224 z-score=-0.448741, p-value=0.347952 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-12-09_03:31 Test no p-value 1 0.005899 2 0.660969 3 0.996969 4 0.379160 5 0.162570 6 0.889840 7 0.015373 8 0.757182 9 0.246408 10 0.170947 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.204425 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-12-09_03:31: (for k>=2, the prob. of a run of length k is 2*k/(k+1)!) Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E 2 66666.67 66867 0.60 66717 0.04 3 25000.00 24927 0.21 24949 0.10 4 6666.67 6601 0.65 6655 0.02 5 1388.89 1349 1.15 1407 0.24 6 238.10 224 0.83 230 0.28 7 34.72 28 1.30 37 0.15 8 4.96 3 0.77 4 0.19 p=0.52063 p=0.01475 Number of rngs required: 686927, p-value: 0.042 RESULTS OF CRAPS TEST for dh-ranFile-2016-12-09_03:31 No. of wins: Observed Expected 98626 98585.9 z-score= 0.180, pvalue=0.57124 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66668 66666.7 0.000 0.000 2 37873 37654.3 1.270 1.270 3 26876 26954.7 0.230 1.500 4 19317 19313.5 0.001 1.501 5 13888 13851.4 0.097 1.597 6 9872 9943.5 0.515 2.112 7 7162 7145.0 0.040 2.152 8 5153 5139.1 0.038 2.190 9 3692 3699.9 0.017 2.207 10 2566 2666.3 3.773 5.980 11 1922 1923.3 0.001 5.981 12 1400 1388.7 0.091 6.072 13 981 1003.7 0.514 6.586 14 764 726.1 1.974 8.560 15 514 525.8 0.266 8.826 16 374 381.2 0.134 8.960 17 270 276.5 0.155 9.115 18 186 200.8 1.095 10.210 19 122 146.0 3.940 14.151 20 98 106.2 0.635 14.786 21 302 287.1 0.772 15.558 Chisq= 15.56 for 20 degrees of freedom, p= 0.25635 SUMMARY of craptest p-value for no. of wins: 0.571242 p-value for throws/game: 0.256349 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-12-09_03:31 No. of wins: Observed Expected 98535 98585.9 z-score=-0.227, pvalue=0.41003 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67052 66666.7 2.227 2.227 2 37915 37654.3 1.805 4.032 3 26704 26954.7 2.332 6.364 4 19317 19313.5 0.001 6.365 5 13637 13851.4 3.319 9.684 6 9692 9943.5 6.363 16.047 7 7188 7145.0 0.258 16.306 8 5216 5139.1 1.152 17.457 9 3694 3699.9 0.009 17.467 10 2614 2666.3 1.026 18.492 11 1838 1923.3 3.786 22.278 12 1403 1388.7 0.146 22.425 13 1000 1003.7 0.014 22.438 14 752 726.1 0.921 23.359 15 529 525.8 0.019 23.378 16 357 381.2 1.530 24.908 17 321 276.5 7.148 32.057 18 193 200.8 0.305 32.362 19 178 146.0 7.021 39.383 20 109 106.2 0.073 39.456 21 291 287.1 0.053 39.509 Chisq= 39.51 for 20 degrees of freedom, p= 0.99424 SUMMARY of craptest p-value for no. of wins: 0.410029 p-value for throws/game: 0.994240 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0048,0.0059,0.0147,0.0154,0.0166,0.0191,0.0270,0.0304,0.0330,0.0380, 0.0416,0.0451,0.0504,0.0516,0.0709,0.0710,0.0716,0.0720,0.0821,0.0854, 0.0885,0.0888,0.0946,0.0995,0.1080,0.1092,0.1182,0.1206,0.1224,0.1266, 0.1293,0.1307,0.1324,0.1339,0.1346,0.1347,0.1363,0.1365,0.1374,0.1400, 0.1405,0.1469,0.1480,0.1488,0.1514,0.1576,0.1626,0.1709,0.1737,0.1852, 0.1874,0.1950,0.1962,0.1990,0.2044,0.2087,0.2125,0.2146,0.2156,0.2204, 0.2204,0.2209,0.2257,0.2284,0.2395,0.2464,0.2512,0.2563,0.2588,0.2612, 0.2677,0.2693,0.2760,0.2777,0.2796,0.2826,0.2856,0.2860,0.2890,0.2926, 0.2977,0.3099,0.3118,0.3132,0.3149,0.3171,0.3198,0.3228,0.3240,0.3243, 0.3292,0.3300,0.3318,0.3319,0.3376,0.3392,0.3400,0.3404,0.3417,0.3440, 0.3449,0.3480,0.3505,0.3657,0.3660,0.3707,0.3789,0.3792,0.3851,0.3859, 0.3866,0.3921,0.3989,0.4052,0.4090,0.4100,0.4105,0.4193,0.4252,0.4329, 0.4499,0.4527,0.4545,0.4575,0.4629,0.4679,0.4702,0.4736,0.4749,0.4800, 0.4887,0.4910,0.4922,0.4928,0.5055,0.5057,0.5069,0.5119,0.5160,0.5185, 0.5198,0.5206,0.5208,0.5210,0.5280,0.5305,0.5357,0.5360,0.5364,0.5364, 0.5406,0.5501,0.5603,0.5673,0.5687,0.5687,0.5695,0.5712,0.5714,0.5738, 0.5774,0.5906,0.5917,0.5936,0.6002,0.6020,0.6130,0.6153,0.6173,0.6358, 0.6391,0.6415,0.6446,0.6464,0.6487,0.6533,0.6565,0.6577,0.6579,0.6606, 0.6610,0.6695,0.6754,0.6825,0.6874,0.6975,0.7009,0.7116,0.7254,0.7260, 0.7292,0.7304,0.7307,0.7307,0.7312,0.7364,0.7385,0.7422,0.7425,0.7429, 0.7446,0.7477,0.7478,0.7561,0.7572,0.7611,0.7748,0.7777,0.7812,0.7932, 0.7956,0.7984,0.7986,0.8055,0.8059,0.8068,0.8074,0.8100,0.8184,0.8232, 0.8267,0.8298,0.8345,0.8403,0.8424,0.8468,0.8501,0.8588,0.8592,0.8609, 0.8622,0.8652,0.8682,0.8695,0.8776,0.8893,0.8898,0.8964,0.8974,0.9086, 0.9099,0.9112,0.9146,0.9149,0.9206,0.9249,0.9257,0.9299,0.9299,0.9315, 0.9321,0.9372,0.9388,0.9407,0.9412,0.9532,0.9599,0.9620,0.9625,0.9647, 0.9658,0.9727,0.9795,0.9801,0.9895,0.9942,0.9970,0.9979,0.9980, Overall p-value after applying KStest on 269 p-values = 0.984750 In response to requests, we have provided a list of all the p-values produced by the tests you have chosen for this run. The individual p-values are supposed to be uniform in [0,1), but they are not necessarily independent. So even though we have applied a KSTEST to the accumulated p-values, the result is not necessarily---even if your file contains truly random bits---uniform in [0,1). But it is probably pretty close, so take that last p-value with a grain of salt. In particular, there may be some values so close to 0 or 1 that the tests they came from should be applied several more times, or new, related tests should be undertaken.